(02) Meta Supervised Learning

Task Definition

First, to understand the Meta-Learning problem, we have to define the concept of a "task".

Definition of a task in supervised learning:

\[\begin{equation} T=\{p(x), p(x|y), \mathcal{L}\} \label{eq:series} \end{equation}\]

Which $p(x)$ represents the probability of the data $x$, $p(y\mid x)$ denotes the probability distribution of the correct label $y$ given the data, and $\mathcal{L}$ represents the loss function.

Therefore, in the case of supervised learning, when each of $p(x), p(y\mid x)$, and $\mathcal{L}$ are defined, we call this a task.

Definition of a task in Multi-task and Meta Learning

\[\begin{equation} T_{1}, T_2, \cdots, T_n \sim P(T) \end{equation}\]

In the context of a supervised learning problem, the definition of a single task refers to the problem of learning from it. However, in Multi-task and Meta-Learning, we aim to solve problems involving multiple tasks, and thus, we can define a task distribution $p(T)$ that allows us to sample from multiple tasks.

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